International Association for Cryptologic Research

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2012-04-11
21:17 [Pub][ePrint]

Dodis and Wichs introduced the notion of a non-malleable extractor to study the problem of privacy amplification with an active adversary. A non-malleable extractor is a much stronger version of a strong extractor. Given a weakly-random string $x$ and a uniformly random seed $y$ as the inputs, the non-malleable extractor $nmExt$ has the property that $nmExt(x,y)$ appears uniform even given $y$ as well as $nmExt(x,A(y))$, for an arbitrary function $A$ with $A(y) \\neq y$. Dodis and Wichs showed that such an object can be used to give optimal privacy amplification protocols with an active adversary.

Previously, there are only two known constructions of non-malleable extractors \\cite{DLWZ11, CRS11}. Both constructions only work for $(n, k)$-sources with $k>n/2$. Interestingly, both constructions are also two-source extractors.

In this paper, we present a strong connection between non-malleable extractors and two-source extractors. The first part of the connection shows that non-malleable extractors can be used to construct two-source extractors. If the non-malleable extractor works for small min-entropy and has a short seed length with respect to the error, then the resulted two-source extractor beats the best known construction of two-source extractors. This partially explains why previous constructions of non-malleable extractors only work for sources with entropy rate $>1/2$, and why explicit non-malleable extractors for small min-entropy may be hard to get.

The second part of the connection shows that certain two-source extractors can be used to construct non-malleable extractors. Using this connection, we obtain the first construction of non-malleable extractors for $k < n/2$. Specifically, we give an unconditional construction for min-entropy $k=(1/2-\\delta)n$ for some constant $\\delta>0$, and a conditional (semi-explicit) construction that can potentially achieve $k=\\alpha n$ for any constant $\\alpha>0$.

We also generalize non-malleable extractors to the case where there are more than one adversarial seeds, and show a similar connection between the generalized non-malleable extractors and two-source extractors.

Finally, despite the lack of explicit non-malleable extractors for arbitrarily linear entropy, we give the first 2-round privacy amplification protocol with asymptotically optimal entropy loss and communication complexity for $(n, k)$ sources with $k=\\alpha n$ for any constant $\\alpha>0$. This dramatically improves previous results and answers an open problem in \\cite{DLWZ11}.

21:17 [Pub][ePrint]

We present the first key-management functionality in the Universal Composability (UC) framework. It allows the enforcement of a wide range of security policies and can be extended by diverse key usage operations with no need to repeat the security proof. We illustrate its use by proving an implementation of a Security API secure with respect to arbitrary key-usage operations and explore a proof technique that allows the storage of cryptographic keys externally, a novel development in the UC framework.

18:17 [Pub][ePrint]

Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key, meaning that anyone can verify a banknote as genuine, not only the bank that printed it, and (2) cryptographically secure, under a \"classical\" hardness assumption that has nothing to do with quantum money. Our scheme is based on hidden subspaces, encoded as the zero-sets of random multivariate polynomials. A main technical advance is to show that the \"black-box\" version of our scheme, where the polynomials are replaced by classical oracles, is unconditionally secure. Previously, such a result had only been known relative to a quantum oracle (and even there, the proof was never published). Even in Wiesner\'s original setting -- quantum money that can only be verified by the bank -- we are able to use our techniques to patch a major security hole in Wiesner\'s scheme. We give the first private-key quantum money scheme that allows unlimited verifications and that remains unconditionally secure, even if the counterfeiter can interact adaptively with the bank. Our money scheme is simpler than previous public-key quantum money schemes, including a knot-based scheme of Farhi et al. The verifier needs to perform only two tests, one in the standard basis and one in the Hadamard basis -- matching the original intuition for quantum money, based on the existence of complementary observables. Our security proofs use a new variant of Ambainis\'s quantum adversary method, and several other tools that might be of independent interest.

18:17 [Pub][ePrint]

In this paper, we present several efficient fault attacks against implementations of RSA-CRT signatures that use modular exponentiation algorithms based on Montgomery multiplication. They apply to any padding function, including randomized paddings, and as such are the

first fault attacks effective against RSA-PSS.

The new attacks work provided that a small register can be forced to either zero, or a constant value, or a value with zero high-order bits. We show that these models are quite realistic, as such faults can be achieved against many proposed hardware designs for RSA signatures.

18:17 [Pub][ePrint]

We present a mechanized proof of the password-based protocol One-Encryption Key Exchange (OEKE) using the computationally-sound protocol prover CryptoVerif. OEKE is a non-trivial protocol, and thus mechanizing its proof provides additional confidence that it is correct.

This case study was also an opportunity to implement several important extensions of CryptoVerif, useful for proving many other protocols. We have indeed extended CryptoVerif to support the computational Diffie-Hellman assumption. We have also added support for proofs that rely on Shoup\'s lemma and additional game transformations. In particular, it is now possible to insert case distinctions manually and to merge cases that no longer need to be distinguished. Eventually, some improvements have been added on the computation of the probability bounds for attacks, providing better reductions. In particular, we improve over the standard computation of probabilities when Shoup\'s lemma is used, which allows us to improve the bound given in a previous manual proof of OEKE, and to show that the adversary can test at most one password per session of the protocol.

In this paper, we present these extensions, with their application to the proof of OEKE. All steps of the proof, both automatic and manually guided, are verified by CryptoVerif.

18:17 [Pub][ePrint]

Since the invention of the Rubik\'s cube by Ern\\\"o~Rubik in $1974$, similar puzzles have been produced, with various number of faces or stickers. We can use these toys to define several problems in computer science, such as go from one state of the puzzle to another one. In this paper, we will classify some of these problems based on the classic Rubik\'s cube or on generalized Rubik\'s Cube. And we will see how we can use them in Zero Knowledge Authentication with a public key in order to achieve a given complexity against the best known attacks (for example $2^{80}$ computations). The efficiency of these schemes, and their possible connection with

NP-complete problems will also be discussed.

18:17 [Pub][ePrint]

Hardware devices can be protected against side-channel attacks by introducing one random mask per sensitive variable.

The computation throughout is unaltered if the shares (masked variable and mask) are processed concomitantly, in two distinct registers.

Nonetheless, this setup can be attacked by a zero-offset second-order CPA attack.

The countermeasure can be improved by manipulating the mask through a bijection $F$,

aimed at reducing the dependency between the shares.

Thus $d$th-order zero-offset attacks, that consist in applying CPA on the $d$th power of the centered side-channel traces,

can be thwarted for $d \\geq 2$ at no extra cost.

We denote by $n$ the size in bits of the shares and call $F$ the transformation function,

that is a bijection of $\\mathbb{F}_2^n$.

In this paper, we explore the functions $F$ that thwart zero-offset HO-CPA of maximal order $d$.

We mathematically demonstrate that optimal choices for $F$ relate to optimal binary codes (in the sense of communication theory).

First, we exhibit optimal linear $F$ functions.

Second, we note that for values of $n$ for which non-linear codes exist with better parameters than linear ones.

These results are exemplified in the case $n=8$, the optimal $F$ can be identified:

it is derived from the optimal rate~$1/2$ binary code of size $2n$, namely the Nordstrom-Robinson $(16, 256, 6)$ code.

This example provides explicitly with the optimal protection that limits to one mask of byte-oriented algorithms such as AES or AES-based SHA-3 candidates.

It protects against all zero-offset HO-CPA attacks of order $d \\leq 5$.

Eventually, the countermeasure is shown to be resilient to imperfect leakage models.

18:17 [Pub][ePrint]

Algebraic attacks are studied as a potential cryptanalytic procedure for various types of ciphers. The XL_SGE algorithm has been recently proposed to improve the complexity of the XL attack. XL_SGE uses structured Gaussian elimination (SGE) during the expansion phase of XL. In this paper, we establish that XL_SGE suffers from some serious drawbacks that impair the effectiveness of SGE-based reduction at all multiplication stages except the first. In order to avoid this problem, we propose several improvements of XL_SGE. Our modifications are based

upon partial monomial multiplication and handling of columns of weight two. Our modified algorithms have been experimentally verified to be substantially superior to XL_SGE.

18:17 [Pub][ePrint]

A protocol has everlasting security if it is secure against

adversaries that are computationally unlimited after the protocol

execution. This models the fact that we cannot predict which

cryptographic schemes will be broken, say, several decades after the

protocol execution. In classical cryptography, everlasting security is

difficult to achieve: even using trusted setup like common reference

strings or signature cards, many tasks such as secure communication

and oblivious transfer cannot be achieved with everlasting security.

An analogous result in the quantum setting excludes protocols based on

common reference strings, but not protocols using a signature card. We

define a variant of the Universal Composability framework, everlasting

quantum-UC, and show that in this model, we can implement secure

communication and general two-party computation using a signature card

as trusted setup.

18:17 [Pub][ePrint]

Cryptographic (or end-to-end) election verification is a promising approach to providing transparent elections in an age of electronic voting technology. In terms of execution time and software complexity however, the technical requirements for conducting a cryptographic election audit can be prohibitive. In an effort to reduce these requirements we present Eperio: a new, provably secure construction for providing a tally that can be efficiently verified using only a small set of primitives. We show how common-place utilities, like the use of file encryption, can further simplify the verification process for election auditors. Using Python, verification code can be expressed in 50 lines of code. Compared to other proposed proof-verification methods for end-to-end election audits, Eperio lowers the technical requirements in terms of execution time, data download times, and code size. As an interesting alternative, we explain how verification can be implemented using TrueCrypt and the built-in functions of a spreadsheet, making Eperio the first end-to-end system to not require special-purpose verification software.

18:17 [Pub][ePrint]

The goal of this paper is to assess the feasibility of two-party secure computation in the presence of a malicious adversary. Prior work has shown the feasibility of billion-gate circuits in the semi-honest model, but only the 35k-gate AES circuit in the malicious model, in part because security in the malicious model is much harder to achieve. We show that by incorporating the best known techniques and parallelizing almost all steps of the resulting protocol, evaluating billion-gate circuits is feasible in the malicious model. Our results are in the standard model (i.e., no common reference strings or PKIs) and, in contrast to prior work, we do not use the random oracle model which has well-established theoretical shortcomings.